There is absolutely no reason that bi-wiring, or any other such connection scheme should effect the heat from your power amplifier. The heat coming from the amp at idle is determined by the standing bias current passing through the output transistors. This would not change with a different wiring scheme. The heat at high signal is totally dependent on the load impedance of the speaker and the power output of the amp at the time.

What this does indicate is that there is possibly something wrong with either your amp, the speakers, or the wiring. If for instance the amplifier was oscillating with your previous setup, that would cause the amp to get hotter, or very hot.

It is also possible that when you changed to bi-wiring, you cleared up a partial short which went unnoticed before.

At any rate, bi-wiring cannot have any effect on the amplifier if everything is operating properly.